相关论文: Finite State Mean Field Games with Common Shocks

In this paper we consider extended stationary mean field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean field…

A notion of incentive for agents is introduced which leads to a very general notion of an equilibrium for a finite game. Sufficient conditions for the existence of these equilibria are given. Known existence theorems are shown to be…

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of…

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi…

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…

In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising…

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…